I have found one but am not sure if there is one before it. My approach has been trial and error but feel there ought to be some kind of strategy. I am guessing the second digit 0?

Any thoughts?

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I have found one but am not sure if there is one before it. My approach has been trial and error but feel there ought to be some kind of strategy. I am guessing the second digit 0?

Any thoughts?

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Which number did you find? How do you suppose to show that there is not one before it?

I have found one but am not sure if there is one before it. My approach has been trial and error but feel there ought to be some kind of strategy. I am guessing the second digit 0?

Any thoughts?

1692 3384 5076

1809 3618 5427

1902 3804 5706

1908 3816 5724

1920 3840 5760

2019 4038 6057

2079 4158 6237

2169 4338 6507

2190 4380 6570

2673 5346 8019

2697 5394 8091

2703 5406 8109

2730 5460 8190

2967 5934 8901

3027 6054 9081

3078 6156 9234

3267 6534 9801

3270 6540 9810

Brute strength. I see no way to nicely "calculate".

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The sum of the digits of all the numbers in column 3 add to 18. Why is that?

1692 3384 5076

1809 3618 5427

1902 3804 5706

1908 3816 5724

1920 3840 5760

2019 4038 6057

2079 4158 6237

2169 4338 6507

2190 4380 6570

2673 5346 8019

2697 5394 8091

2703 5406 8109

2730 5460 8190

2967 5934 8901

3027 6054 9081

3078 6156 9234

3267 6534 9801

3270 6540 9810

Brute strength. I see no way to nicely "calculate".

No idea...good stuff for your "whiteboard"The sum of the digits of all the numbers in column 3 add to 18. Why is that?

Seems to be for that "case" only; tried a few others,

like 2789: 2789*3 = 8367: sum digits = 24

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But this is not the special number that fits our case.No idea...good stuff for your "whiteboard"

Seems to be for that "case" only; tried a few others,

like 2789: 2789*3 = 8367: sum digits = 24

That's what I meant with "Seems to be for that "case" only".But this is not the special number that fits our case.

I was unclearly saying that the "18" result is only when all 10 digits appear.

Which number did you find? How do you suppose to show that there is not one before it?

The one i got was 3027! But it was mostly guess work!

Someone sent it to me. And i couldn't see an interesting way to approach it so wondered if i was missing something!Any "reason" you posted this?

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Denis, can you please do me a favor and run your program for more numbers of this type?That's what I meant with "Seems to be for that "case" only".

I was unclearly saying that the "18" result is only when all 10 digits appear.

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If you play LOTTO with those numbers - he can demand a cut of the winnings!!Denis, can you please do me a favor and run your program for more numbers of this type?

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He really is a demanding person, isn't he?If you play LOTTO with those numbers - he can demand a cut of the winnings!!

Happy New Years!!

There's no more.Denis, can you please do me a favor and run your program for more numbers of this type?

Didn't write a program: calculated those in my head during my morning walk :lol:

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1234567890 2469135780 3703703670-----sum of digits of the last number is 36, which is 2*18. Strange

9012345678 ..... ..... sum of digits of the last number is 36, which is 2*18. Strange

If this pattern of multiples of 18 will continue, then I will like to try to prove this with minimal help. So if someone sees the prove, can you please give me some leading hints.

9012345678 ..... ..... sum of digits of the last number is 36, which is 2*18. Strange

If this pattern of multiples of 18 will continue, then I will like to try to prove this with minimal help. So if someone sees the prove, can you please give me some leading hints.

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What if I say please?? Please run your program. And I was joking about you being a demanding person.There's no more.

Didn't write a program: calculated those in my head during my morning walk :lol:

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I guess what you are saying is true but there are 5, 6, 7, .... digit numbers which you did not find. This really seems like an interesting problem even if does not go on for ever and I'd like to look into this. After all, this is what real mathematicians do (not that I am one).What do you mean Steve?

There are no more cases of 3 4digit numbers

containing all the 10 digits (at least once each),

where (1st number = a) the 3 numbers are a, 2a and 3a.

BUT I was NOT looking for those: I was looking for 3 numbers that areI guess what you are saying is true but there are 5, 6, 7, .... digit numbers which you did not find.

each 4 digits, NOTHING else. Which meant the lower was in range

1000 to 3333, meaning high case of 3333,6666,9999.

Sorry 'bout dat, chief...as Maxwell Smart would say...

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Look Jackson, I am asking you for a favor. Can you modify yourBUT I was NOT looking for those: I was looking for 3 numbers that are

each 4 digits, NOTHING else. Which meant the lower was in range

1000 to 3333, meaning high case of 3333,6666,9999.

Sorry 'bout dat, chief...as Maxwell Smart would say...